Question: Simplify the following expression: $q = \dfrac{2y^2 + 30y + 108}{y + 6} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $2$ , so we can rewrite the expression: $ q =\dfrac{2(y^2 + 15y + 54)}{y + 6} $ Then we factor the remaining polynomial: $y^2 + {15}y + {54} $ ${6} + {9} = {15}$ ${6} \times {9} = {54}$ $ (y + {6}) (y + {9}) $ This gives us a factored expression: $\dfrac{2(y + {6}) (y + {9})}{y + 6}$ We can divide the numerator and denominator by $(y - 6)$ on condition that $y \neq -6$ Therefore $q = 2(y + 9); y \neq -6$